We have explored two of the three dimensions in
mu,
md,
me space:
md -
mu
and me. In addition
there is a third dimension to explore,
md +
mu. This
quantity affects the
pion mass and therefore the range of the nuclear interactions;
this does not affect the np stability arguments
but does affect the D stability.

The dependence on this
third dimension of fermion mass variation can be estimated
through the effect of changes in
nucleon potential through the pion mass,
m2 (mu +
md)
QCD. In this framework
Agrawal et al. (1998)
investigated the effect of
varying the Higgs expectation value v, which changes all the fermion
masses in proportion. Using a simple model of
the deuteron potential (range 2 fm, depth 35MeV)
they found no bound
states anymore if the range is reduced by 20%, or the quark
mass sum is increased by 40%. This corresponds to a change
v / v0 = 1.4 or
mi = 0.4
mi, or approximately
md +
mu 0.4 (md +
mu)
7 MeV.
(See also the earlier discussion of light nuclei stability by
Pochet et al. 1991).
On the side of decreasing quark masses or increasing range (i.e.
md +
mu
< 0), the effects are opposite; at about
md +
mu -0.25 (md
+ mu)
-4 MeV,
the diproton 2He or the dineutron become bound
(Dyson 1971).
(Which one is stable depends on the mass difference
md-u.)
However, a tighter constraint in this dimension is likely to arise from
the behavior of heavier nuclei.